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Fractions Numerator and denominator Place valueHere you will learn about decimal place value, including the names and values of the different positions.
Students will first learn about decimal place value as part of their work with numbers and operations in base ten in elementary school.
Decimal place value extends our understanding of place value to the decimal system, which are the digits to the right of the decimal point.
To do this, look at the connection between fractions and decimals.
For example,
This model shows \cfrac{4}{10}.
We can also write this as the decimal 0.4. We read it as โfour-tenths,โ just like the fraction.
That is because the first decimal place is tenths.
Letโs look at the next decimal place.
For example,
This model shows \cfrac{4}{100}.
We can also write this as the decimal 0.04. We read it as โfour-hundredths,โ just like the fraction.
That is because the second decimal place is hundredths.
Letโs look at the next decimal place.
For example,
This model shows \cfrac{4}{1,000}.
We can also write this as the decimal 0.004. We read it as โfour-thousandths,โ just like the fraction.
That is because the third decimal place is thousandths.
Here are the first three decimal place values. They show us the value of each digit in the number.
Notice the pattern in the denominators:
to to
As the places become smaller, each is \cfrac{1}{10} the size of the place to its left.
As the places become larger, each is 10 times the size of the place to its right.
These are the same patterns you see with whole numbers.
How does this relate to 4th grade math and 5th grade math?
In order to write a fraction as a decimal:
In order to write a fraction as a decimal:
In order to write the value of a digit in a decimal number:
In order to compare the value of a digit in two decimal numbers:
Use this worksheet to check your grade 4 and 5 studentsโ understanding of decimal place value. 15 questions with answers to identify areas of strength and support!
DOWNLOAD FREEUse this worksheet to check your grade 4 and 5 studentsโ understanding of decimal place value. 15 questions with answers to identify areas of strength and support!
DOWNLOAD FREEWrite \cfrac{2}{10} as a decimal.
\cfrac{2}{10} is 2 tenths.
2Place the numerator of the fraction on the place value chart.
Put a 2 in the tenths place.
3Write the decimal number.
\cfrac{2}{10} written as a decimal is 0.2
Write \cfrac{51}{100} as a decimal.
Write the fraction in words.
\cfrac{51}{100} is 51 hundredths.
Place the numerator of the fraction on the place value chart.
The model shows \cfrac{51}{100}.
In the model there are 5 full columns of 10, which is equal to 5 tenths.
So to write this decimal, put a 5 in the tenths place and 1 in the hundredths place.
Write the decimal number.
\cfrac{51}{100} written as a decimal is 0.51
*Notice there is only one digit in each place, just like with whole numbers.
Write 0.22 as a fraction.
Write the decimal in words using a place value chart.
0.22 is 22 hundredths.
The digits of the decimal will be the numerator, and the denominator is where the last digit of the decimal is in the place value chart.
The model shows 22 hundredths.
The 22 in the decimal is the numerator.
The last place value position is hundredths (which is also the size of the 22 parts), so this is the denominator.
Write the fraction.
0.22=\cfrac{22}{100}
What is the value of the digit 3 in 0.13?
Locate the digit within the number.
Use the place value chart to find the position.
Write the value of the digit.
The value of the digit 3 is 0.03 or \cfrac{3}{100}.
What is the value of the digit 7 in 0.75?
Locate the digit within the number.
Use the place value chart to find the position.
Write the value of the digit.
The value of the digit 7 is 0.7 or \cfrac{7}{10}.
Compare the value of each digit 1 in the number 0.101.
Locate the digits within the number(s).
Use the place value chart to find the positions.
Compare how many times bigger or smaller the positions are.
In 0.101, there is a digit 1 in the tenths position and in the thousandths position.
0.1 is 100 times greater than 0.001.
0.001 is 100 times smaller than 0.1. The 1 in the thousandths is \cfrac{1}{100} the value of the 1 in the tenths.
1. Write \cfrac{8}{10} as a decimal.
\cfrac{8}{10} is 8 tenths. Put an 8 in the tenths place.
\cfrac{8}{10} written as a decimal is 0.8
2. Write \cfrac{62}{100} as a decimal.
\cfrac{62}{100} is 62 hundredths.
The model shows \cfrac{62}{100}.
In the model there are 6 full columns of 10, which is equal to 6 tenths.
So to write this decimal, put a 6 in the tenths place and 2 in the hundredths place.
\cfrac{62}{100} written as a decimal is 0.62
3. Write 0.19 as a fraction.
0.19 is 19 hundredths.
The model shows 19 hundredths.
The 19 in the decimal is the numerator.
The last place value position is hundredths (which is also the size of the 19 parts), so this is the denominator.
0.19=\cfrac{19}{100}
4. What is the value of the digit 4 in 0.054?
4 tenths
4 thousandths
4 hundredths
Locate the digit within the number.
Use the place value chart to find the position.
The value of the digit 4 is 4 thousandths (0.004 or \cfrac{4}{1,000}).
5. Choose the correct comparison of each digit 8โs value in the numbers 0.8 and 0.18.
The 8 in 0.8 is 100 times less
The 8 in 0.18 is 10 times more
The 8 in 0.8 is 10 times more
The 8 in 0.18 is 100 times less
Locate the digits within the number(s).
Use the place value chart to find the positions.
In 0.8, \, 8 is in the tenths position. In 0.18, \, 8 is in the hundredths position.
Tenths are 10 times more than hundredths, so the 8 in 0.8 is 10 times more.
6. Choose the correct comparison of the digit 3โs values in the number 0.033.
The 3 in the thousandths is \cfrac{1}{10} the size of the 3 in the hundredths
The 3 in the thousandths is 100 times smaller than the 3 in the hundredths
The 3 in the hundredths is 10 times smaller than the 3 in the tenths
The 3 in the hundredths is \cfrac{1}{10} the size of the 3 in the thousandths
Locate the digits within the number(s).
Use the place value chart to find the positions.
In 0.033, there is a digit 3 in the hundredths position and in the thousandths position.
Thousandths are \cfrac{1}{10} the size of hundredths, so the 3 in the thousandths is \cfrac{1}{10} of the 3 in the hundredths.
We use a Base Ten number system, meaning each place value position is a grouping of 10. That is why all of the place value positions (like the tenths place or hundredths place) are multiples of 10.
They are similar because they can both be used to represent parts. For example, the fraction \cfrac{3}{10} represents a part ( 3 tenths) and the decimal 0.3 represents a part ( 3 tenths).
Decimal place value gives meaning to the digits in each position and helps you understand the size of a number. Understanding decimal place value can help you when comparing or ordering decimals and is also necessary to know when calculating with decimal numbers.
In the Common Core, fifth grade students are expected to know and use the tenths place, the hundredths place, and the thousandths place. Sixth graders extend this to even smaller positions. However, it can vary from state to state, so be mindful of your stateโs standard expectations.
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